We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in practice. Rather, we use light-emitting diodes (LEDs) to illuminate the scene to reconstruct. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how to calibrate its parameters. Then, we discuss two state-of-the-art numerical solutions. The first one alternatingly estimates the albedo and the normals, and then integrates the normals into a depth map. It is shown empirically to be independent from the initialization, but convergence of this sequential approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of PDEs which are partially linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence is not established either. Therefore, we introduce a provably convergent alternating reweighted least-squares scheme for solving the original system of PDEs, without resorting to image ratios for linearization. Finally, we extend this study to the case of RGB images.
Most conventional photometric stereo algorithms inversely solve a BRDF-based image formation model. However, the actual imaging process is often far more complex due to the global light transport on the non-convex surfaces. This paper presents a photometric stereo network that directly learns relationships between the photometric stereo input and surface normals of a scene. For handling unordered, arbitrary number of input images, we merge all the input data to the intermediate representation called {\it observation map} that has a fixed shape, is able to be fed into a CNN. To improve both tra…
University of Cambridge（剑桥大学）；Toshiba Research（东芝研究院）
Highly accurate 3D volumetric reconstruction is still an open research topic where the main difficulty is usually related to merging some rough estimations with high frequency details. One of the most promising methods is the fusion between multi-view stereo and photometric stereo images. Beside the intrinsic difficulties that multi-view stereo and photometric stereo in order to work reliably, supplementary problems arise when considered together. In this work, we present a volumetric approach to the multi-view photometric stereo problem. The key point of our method is the signed distance fiel…
This paper presents a near-light photometric stereo method that faithfully preserves sharp depth edges in the 3D reconstruction. Unlike previous methods that rely on finite differentiation for approximating depth partial derivatives and surface normals, we introduce an analytically differentiable neural surface in near-light photometric stereo for avoiding differentiation errors at sharp depth edges, where the depth is represented as a neural function of the image coordinates. By further formulating the Lambertian albedo as a dependent variable resulting from the surface normal and depth, our …
This paper solves the Sparse Photometric stereo through Lighting Interpolation and Normal Estimation using a generative Network (SPLINE-Net). SPLINE-Net contains a lighting interpolation network to generate dense lighting observations given a sparse set of lights as inputs followed by a normal estimation network to estimate surface normals. Both networks are jointly constrained by the proposed symmetric and asymmetric loss functions to enforce isotropic constrain and perform outlier rejection of global illumination effects. SPLINE-Net is verified to outperform existing methods for photometric …
This paper tackles the task of uncalibrated photometric stereo for 3D object reconstruction, where both the object shape, object reflectance, and lighting directions are unknown. This is an extremely difficult task, and the challenge is further compounded with the existence of the well-known generalized bas-relief (GBR) ambiguity in photometric stereo. Previous methods to resolve this ambiguity either rely on an overly simplified reflectance model, or assume special light distribution. We propose a new method that jointly optimizes object shape, light directions, and light intensities, all und…
Photometric stereo provides an important method for high-fidelity 3D reconstruction based on multiple intensity images captured under different illumination directions. In this paper, we present a complete framework, including a multilight source illumination and acquisition hardware system and a two-stage convolutional neural network (CNN) architecture, to construct inter- and intraframe representations for accurate normal estimation of non-Lambertian objects. We experimentally investigate numerous network design alternatives for identifying the optimal scheme to deploy inter- and intraframe …
University of Maryland（马里兰大学）；TU Dresden（德累斯顿工业大学）；Weizmann Institute of Science（魏茨曼科学研究学院）
We introduce a new, integrated approach to uncalibrated photometric stereo. We perform 3D reconstruction of Lambertian objects using multiple images produced by unknown, directional light sources. We show how to formulate a single optimization that includes rank and integrability constraints, allowing also for missing data. We then solve this optimization using the Alternate Direction Method of Multipliers (ADMM). We conduct extensive experimental evaluation on real and synthetic data sets. Our integrated approach is particularly valuable when performing photometric stereo using as few as 4-6 …
The University of Hong Kong（香港大学）；University of Oxford（牛津大学）；Peking University（北京大学）；Peng Cheng Laboratory（鹏程实验室）；Osaka University（大阪大学）
This paper proposes an uncalibrated photometric stereo method for non-Lambertian scenes based on deep learning. Unlike previous approaches that heavily rely on assumptions of specific reflectances and light source distributions, our method is able to determine both shape and light directions of a scene with unknown arbitrary reflectances observed under unknown varying light directions. To achieve this goal, we propose a two-stage deep learning architecture, called SDPS-Net, which can effectively take advantage of intermediate supervision, resulting in reduced learning difficulty compared to a …
Cambridge Research Laboratory（剑桥研究实验室）；Toshiba Europe Ltd.（东芝欧洲有限公司）；University of Cambridge（剑桥大学）
Reconstructing the 3D shape of an object using several images under different light sources is a very challenging task, especially when realistic assumptions such as light propagation and attenuation, perspective viewing geometry and specular light reflection are considered. Many of works tackling Photometric Stereo (PS) problems often relax most of the aforementioned assumptions. Especially they ignore specular reflection and global illumination effects. In this work, we propose the first CNN based approach capable of handling these realistic assumptions in Photometric Stereo. We leverage rec…
Methods for 3D reconstruction such as Photometric stereo recover the shape and reflectance properties using multiple images of an object taken with variable lighting conditions from a fixed viewpoint. Photometric stereo assumes that a scene is illuminated only directly by the illumination source. As result, indirect illumination effects due to inter-reflections introduce strong biases in the recovered shape. Our suggested approach is to recover scene properties in the presence of indirect illumination. To this end, we proposed an iterative PS method combined with a reverted Monte-Carlo ray tra…
Obtaining dense 3D reconstrution with low computational cost is one of the important goals in the field of SLAM. In this paper we propose a dense 3D reconstruction framework from monocular multispectral video sequences using jointly semi-dense SLAM and Multispectral Photometric Stereo approaches. Starting from multispectral video, SALM (a) reconstructs a semi-dense 3D shape that will be densified;(b) recovers relative sparse depth map that is then fed as prioris into optimization-based multispectral photometric stereo for a more accurate dense surface normal recovery;(c)obtains camera pose tha…
Three-dimensional reconstruction of objects from shading information is a challenging task in computer vision. As most of the approaches facing the Photometric Stereo problem use simplified far-field assumptions, real-world scenarios have essentially more complex physical effects that need to be handled for accurately reconstructing the 3D shape. An increasing number of methods have been proposed to address the problem when point light sources are assumed to be nearby the target object. The proximity of the light sources complicates the modeling of the image formation as the light behaviour re…
Computer Vision Group, Technical University of Munich（慕尼黑工业大学计算机视觉组）；Erasmus Mundus Masters in Vision and Robotics (VIBOT)（伊拉斯谟世界计划视觉与机器人硕士项目（VIBOT））
A novel depth super-resolution approach for RGB-D sensors is presented. It disambiguates depth super-resolution through high-resolution photometric clues and, symmetrically, it disambiguates uncalibrated photometric stereo through low-resolution depth cues. To this end, an RGB-D sequence is acquired from the same viewing angle, while illuminating the scene from various uncalibrated directions. This sequence is handled by a variational framework which fits high-resolution shape and reflectance, as well as lighting, to both the low-resolution depth measurements and the high-resolution RGB ones. …
The University of Hong Kong（香港大学）；University of Oxford（牛津大学）
This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not requi…
Photometric stereo, a problem of recovering 3D surface normals using images of an object captured under different lightings, has been of great interest and importance in computer vision research. Despite the success of existing traditional and deep learning-based methods, it is still challenging due to: (i) the requirement of three or more differently illuminated images, (ii) the inability to model unknown general reflectance, and (iii) the requirement of accurate 3D ground truth surface normals and known lighting information for training. In this work, we attempt to address an under-explored …
Event-based Photometric Stereo via Rotating Illumination and Per-Pixel Learning
Department of Mechanical Engineering, Yonsei University（延世大学机械工程系）；Department of Electrical and Electronic Engineering, Yonsei University（延世大学电气电子工程系）；Department of Data Science and AI, Monash University（墨尔本大学数据科学与人工智能系）；Meta Reality Labs（Meta现实实验室）
Existing deep calibrated photometric stereo networks basically aggregate observations under different lights based on the pre-defined operations such as linear projection and max pooling. While they are effective with the dense capture, simple first-order operations often fail to capture the high-order interactions among observations under small number of different lights. To tackle this issue, this paper presents a deep sparse calibrated photometric stereo network named {\it PS-Transformer} which leverages the learnable self-attention mechanism to properly capture the complex inter-image inte…
Peking University（北京大学）；Osaka University（大阪大学）；The Chinese University of Hong Kong Shenzhen（香港中文大学（深圳））
Multispectral photometric stereo(MPS) aims at recovering the surface normal of a scene from a single-shot multispectral image captured under multispectral illuminations. Existing MPS methods adopt the Lambertian reflectance model to make the problem tractable, but it greatly limits their application to real-world surfaces. In this paper, we propose a deep neural network named NeuralMPS to solve the MPS problem under general non-Lambertian spectral reflectances. Specifically, we present a spectral reflectance decomposition(SRD) model to disentangle the spectral reflectance into geometric compon…
We present a new color photometric stereo (CPS) method that recovers high quality, detailed 3D face geometry in a single shot. Our system uses three uncalibrated near point lights of different colors and a single camera. For robust self-calibration of the light sources, we use 3D morphable model (3DMM) and semantic segmentation of facial parts. We address the spectral ambiguity problem by incorporating albedo consensus, albedo similarity, and proxy prior into a unified framework. We avoid the need for spatial constancy of albedo; instead, we use a new measure for albedo similarity that is base…
Kyoto University（京都大学）；OMRON SINIC X Corp.（欧姆龙SINIC X公司）
Images captured in participating media such as murky water, fog, or smoke are degraded by scattered light. Thus, the use of traditional three-dimensional (3D) reconstruction techniques in such environments is difficult. In this paper, we propose a photometric stereo method for participating media. The proposed method differs from previous studies with respect to modeling shape-dependent forward scatter. In the proposed model, forward scatter is described as an analytical form using lookup tables and is represented by spatially-variant kernels. We also propose an approximation of a large-scale …
ETH Zürich（苏黎世联邦理工学院）；Google Research（谷歌研究院）；KU Leuven（鲁汶大学）
We present a modern solution to the multi-view photometric stereo problem (MVPS). Our work suitably exploits the image formation model in a MVPS experimental setup to recover the dense 3D reconstruction of an object from images. We procure the surface orientation using a photometric stereo (PS) image formation model and blend it with a multi-view neural radiance field representation to recover the object's surface geometry. Contrary to the previous multi-staged framework to MVPS, where the position, iso-depth contours, or orientation measurements are estimated independently and then fused late…
Uncalibrated photometric stereo is proposed to estimate the detailed surface normal from images under varying and unknown lightings. Recently, deep learning brings powerful data priors to this underdetermined problem. This paper presents a new method for deep uncalibrated photometric stereo, which efficiently utilizes the inter-image representation to guide the normal estimation. Previous methods use optimization-based neural inverse rendering or a single size-independent pooling layer to deal with multiple inputs, which are inefficient for utilizing information among input images. Given multi…
Computer Vision Lab ETH Zürich（苏黎世联邦理工学院计算机视觉实验室）；Google Research（谷歌研究院）；KU Leuven（鲁汶大学）
This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth surface normals of the object or both. However, in practice, it is challenging to procure both of this information precisely, which restricts the broader adoption of photometric stereo algorithms for vision application. To bypass this difficulty, we propose an uncalibrated neural inverse rendering approach to this problem. Our method first estimates the light di…
Uncalibrated photometric stereo (UPS) is challenging due to the inherent ambiguity brought by the unknown light. Although the ambiguity is alleviated on non-Lambertian objects, the problem is still difficult to solve for more general objects with complex shapes introducing irregular shadows and general materials with complex reflectance like anisotropic reflectance. To exploit cues from shadow and reflectance to solve UPS and improve performance on general materials, we propose DANI-Net, an inverse rendering framework with differentiable shadow handling and anisotropic reflectance modeling. Un…
University of Science and Technology of China（中国科学技术大学）；Cardiff University（卡迪夫大学）
Recently, 3D face reconstruction from a single image has achieved great success with the help of deep learning and shape prior knowledge, but they often fail to produce accurate geometry details. On the other hand, photometric stereo methods can recover reliable geometry details, but require dense inputs and need to solve a complex optimization problem. In this paper, we present a lightweight strategy that only requires sparse inputs or even a single image to recover high-fidelity face shapes with images captured under near-field lights. To this end, we construct a dataset containing 84 differ…
Photometric stereo is a method that seeks to reconstruct the normal vectors of an object from a set of images of the object illuminated under different light sources. While effective in some situations, classical photometric stereo relies on a diffuse surface model that cannot handle objects with complex reflectance patterns, and it is sensitive to non-idealities in the images. In this work, we propose a novel approach to photometric stereo that relies on dictionary learning to produce robust normal vector reconstructions. Specifically, we develop two formulations for applying dictionary learn…
Brandenburg University of Technology Cottbus-Senftenberg（科特布斯-森夫滕贝格勃兰登堡工业大学）
Photometric stereo refers to the process to compute the 3D shape of an object using information on illumination and reflectance from several input images from the same point of view. The most often used reflectance model is the Lambertian reflectance, however this does not include specular highlights in input images. In this paper we consider the arising non-linear optimisation problem when employing Blinn-Phong reflectance for modeling specular effects. To this end we focus on the regularising Levenberg-Marquardt scheme. We show how to derive an explicit bound that gives information on the co…
Photometric stereo is a method for estimating the normal vectors of an object from images of the object under varying lighting conditions. Motivated by several recent works that extend photometric stereo to more general objects and lighting conditions, we study a new robust approach to photometric stereo that utilizes dictionary learning. Specifically, we propose and analyze two approaches to adaptive dictionary regularization for the photometric stereo problem. First, we propose an image preprocessing step that utilizes an adaptive dictionary learning model to remove noise and other non-ideal…
Deep Learning Methods for Calibrated Photometric Stereo and Beyond
Nanyang Technological University（南洋理工大学）；The Hong Kong Polytechnic University（香港理工大学）；Shenzhen University（深圳大学）；University of Leicester（莱斯特大学）；Ocean University of China（中国海洋大学）；Peking University（北京大学）
Technical University of Munich（慕尼黑工业大学）；Normandie Univ.（诺曼底大学）；UNICAEN（卡昂诺曼底大学）；ENSICAEN（卡昂国立高等工程师学校）；CNRS（法国国家科学研究中心）
Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indica…
Photometric Stereo methods seek to reconstruct the 3d shape of an object from motionless images obtained with varying illumination. Most existing methods solve a restricted problem where the physical reflectance model, such as Lambertian reflectance, is known in advance. In contrast, we do not restrict ourselves to a specific reflectance model. Instead, we offer a method that works on a wide variety of reflectances. Our approach uses a simple yet uncommonly used property of the problem - the sought after normals are points on a unit hemisphere. We present a novel embedding method that maps pix…
Pose estimation and map building are central ingredients of autonomous robots and typically rely on the registration of sensor data. In this paper, we investigate a new metric for registering images that builds upon on the idea of the photometric error. Our approach combines a gradient orientation-based metric with a magnitude-dependent scaling term. We integrate both into stereo estimation as well as visual odometry systems and show clear benefits for typical disparity and direct image registration tasks when using our proposed metric. Our experimental evaluation indicats that our metric lead…
Uncalibrated photometric stereo (UPS) is challenging due to the inherent ambiguity brought by unknown light. Existing solutions alleviate the ambiguity by either explicitly associating reflectance to light conditions or resolving light conditions in a supervised manner. This paper establishes an implicit relation between light clues and light estimation and solves UPS in an unsupervised manner. The key idea is to represent the reflectance as four neural intrinsics fields, i.e., position, light, specular, and shadow, based on which the neural light field is implicitly associated with light clue…
The University of Hong Kong（香港大学）；University of Oxford（牛津大学）；Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；Osaka University（大阪大学）
This paper addresses the problem of photometric stereo, in both calibrated and uncalibrated scenarios, for non-Lambertian surfaces based on deep learning. We first introduce a fully convolutional deep network for calibrated photometric stereo, which we call PS-FCN. Unlike traditional approaches that adopt simplified reflectance models to make the problem tractable, our method directly learns the mapping from reflectance observations to surface normal, and is able to handle surfaces with general and unknown isotropic reflectance. At test time, PS-FCN takes an arbitrary number of images and thei…
Toshiba Europe Ltd（东芝欧洲有限公司）；University of Cambridge（剑桥大学）
Reconstructing the 3D shape of an object using several images under different light sources is a very challenging task, especially when realistic assumptions such as light propagation and attenuation, perspective viewing geometry and specular light reflection are considered. Many of works tackling Photometric Stereo (PS) problems often relax most of the aforementioned assumptions. Especially they ignore specular reflection and global illumination effects. In this work, we propose a CNN-based approach capable of handling these realistic assumptions by leveraging recent improvements of deep neur…
ETH Zürich（苏黎世联邦理工学院）；Google Research（谷歌研究院）；KU Leuven（鲁汶大学）
Multi-view photometric stereo (MVPS) is a preferred method for detailed and precise 3D acquisition of an object from images. Although popular methods for MVPS can provide outstanding results, they are often complex to execute and limited to isotropic material objects. To address such limitations, we present a simple, practical approach to MVPS, which works well for isotropic as well as other object material types such as anisotropic and glossy. The proposed approach in this paper exploits the benefit of uncertainty modeling in a deep neural network for a reliable fusion of photometric stereo (…
We present a method to capture both 3D shape and spatially varying reflectance with a multi-view photometric stereo (MVPS) technique that works for general isotropic materials. Our algorithm is suitable for perspective cameras and nearby point light sources. Our data capture setup is simple, which consists of only a digital camera, some LED lights, and an optional automatic turntable. From a single viewpoint, we use a set of photometric stereo images to identify surface points with the same distance to the camera. We collect this information from multiple viewpoints and combine it with structu…
We present a single-shot system to recover surface geometry of objects with spatially-varying albedos, from images captured under a calibrated RGB photometric stereo setup---with three light directions multiplexed across different color channels in the observed RGB image. Since the problem is ill-posed point-wise, we assume that the albedo map can be modeled as piece-wise constant with a restricted number of distinct albedo values. We show that under ideal conditions, the shape of a non-degenerate local constant albedo surface patch can theoretically be recovered exactly. Moreover, we present …
This paper tackles a new photometric stereo task, named universal photometric stereo. Unlike existing tasks that assumed specific physical lighting models; hence, drastically limited their usability, a solution algorithm of this task is supposed to work for objects with diverse shapes and materials under arbitrary lighting variations without assuming any specific models. To solve this extremely challenging task, we present a purely data-driven method, which eliminates the prior assumption of lighting by replacing the recovery of physical lighting parameters with the extraction of the generic l…
ETH Zürich（苏黎世联邦理工学院）；Google Research（谷歌研究院）；KU Leuven（鲁汶大学）
This paper presents a simple and effective solution to the longstanding classical multi-view photometric stereo (MVPS) problem. It is well-known that photometric stereo (PS) is excellent at recovering high-frequency surface details, whereas multi-view stereo (MVS) can help remove the low-frequency distortion due to PS and retain the global geometry of the shape. This paper proposes an approach that can effectively utilize such complementary strengths of PS and MVS. Our key idea is to combine them suitably while considering the per-pixel uncertainty of their estimates. To this end, we estimate …
Photometric Stereo (PS) under outdoor illumination remains a challenging, ill-posed problem due to insufficient variability in illumination. Months-long capture sessions are typically used in this setup, with little success on shorter, single-day time intervals. In this paper, we investigate the solution of outdoor PS over a single day, under different weather conditions. First, we investigate the relationship between weather and surface reconstructability in order to understand when natural lighting allows existing PS algorithms to work. Our analysis reveals that partially cloudy days improve…
The problem of estimating a surface shape from its observed reflectance properties still remains a challenging task in computer vision. The presence of global illumination effects such as inter-reflections or cast shadows makes the task particularly difficult for non-convex real-world surfaces. State-of-the-art methods for calibrated photometric stereo address these issues using convolutional neural networks (CNNs) that primarily aim to capture either the spatial context among adjacent pixels or the photometric one formed by illuminating a sample from adjacent directions. In this paper, we bri…
